A Mathematical Model of the Achilles tendon in humans

The purpose of this study is to develop a musculoskeletal model of the human Achilles tendon. An experimental method of obtaining parameter values for the mechanical characteristics of the Achilles tendon and the gastrocnemius muscle is presented. Four healthy subjects were asked to take part in experiments where plantar flexion and dorsiflexion of the foot were studied. Anatomical lengths of different parts of the leg and the foot of each subject were determined by direct measurement and further mathematical calculations. 3D motion capture was used to obtain measurements of forces, moments and angles for the ankle as well as ground reaction forces. Angle trajectories of the ankle joint along with trajectories of the movement of the heel and the Achilles tendon were reconstructed from the data captured for each subject. Parameter estimation was conducted in order to obtain the spring constants and damping coefficients of a Hill-type muscle model used to describe the relationship between the gastrocnemius muscle and the Achilles tendon. Structural identifiability analysis was performed in order to determine if the model parameters were uniquely identifiable for the system model and observations available.